SWIMMING Yukio is keeping track of the number of calories she
burns while swimming freestyle laps. The number of calories she
burns can be represented by a function. Sketch a graph that shows
the number of calories burned y as a function of time x, in hours.
y-Intercept: No calories burned when she has swum for 0 hours.
Linear or Nonlinear: The graph of the function is linear.
Positive: for time greater than 0
Increasing: for time greater than 0
End Behavior: As the number of hours she has swum increases, the
number of calories burned increases.

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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Answer:

486÷27=-18

Step-by-step explanation:

you would divide 27 with numbers until you get -18

Answer:

1/5

Step-by-step explanation:

20*5 = 100, so 20 is 1/5

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

the ratio is 4:15

what times 4 is 10? (10/4) 2.5 times 4 is 10.

10: 15*2.5

10:37.5

they are 37.5 km away in reality i hope this helped and i hope it is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

5m +5n+6m−4n

Next, group like terms:

5m+6m+5n−4n

Now, combine like terms:

(5+6)m+(5−4)n

11m+1n

11m+n

Answer:

\(\large\boxed{\mathtt{9^{8}}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked to simplify the given expression.}\)

\(\textsf{Let's begin by understand an important rule for problems like these.}\)

\(\mathtt{9^{3} \times 9^{5} = 9^{?}}\)

\(\large\underline{\textsf{We should remember that;}}\)

\(\textsf{When exponents multiply, they \underline{add}.}\)

\(\large\underline{\textsf{Why?}}\)

\(\textsf{If not, then the answer will be incorrect. Let's identify why in an example.}\)

\(\large\underline{\textsf{Bad Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2 \times 5 =10}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \neq 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\large\underline{\textsf{Good Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2+5=7}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\textsf{Let's follow the good example!}\)

\({\mathtt{9^{3} \times 9^{5} = 9^{3 + 5=8}}\)

\(\textsf{This means that;}\)

\(\mathtt{9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9.}\)

\(\large\boxed{\mathtt{9^{8}}}\)

\(\huge\text{Hey there!}\)

\(\mathsf{9^3 \times 9^5}\\\mathsf{= 9\times 9 \times 9\ \boxed{\times}\ 9\times 9\times 9 \times 9 \times 9}\\\mathsf{= 81\times 9\ \boxed{\times}\ 81\times81\times9}\\\mathsf{= 729\ \boxed{\times}\ 6,561\times 9}\\\mathsf{= 729\ \boxed{\times}\ 59,049}\\\mathsf{= 43,046,721}\\\mathsf{= 9^3 \times 9^5 \rightarrow 9^{3 + 5}\rightarrow 9^8}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{9^8}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

Principal = 20833.334

Step-by-step explanation:

simple interest = $5000.

Rate = 3%

Time = 8 years.

Principal = ?

Principal =

\( = \frac{100 \times simple \: interest}{r \times t} \\ = \frac{100 \times5000 }{3 \times 8} \\ = \frac{500000}{24 \\ } \\ = 20833.334\)

Principal = $20833.334.

The answer choice which gives the best-example of the "random-sample" is (c) Ask 10 people from each "grade-level" at Allison's school about how many games they have on their phones.

A "Random-Sample" is a subset of a larger population which is chosen in such a way that each member of the population has an equal chance of being selected.

The Option (c) :  gives the best example of a random sample that Allison could use to help answer her question. By asking 10 people from each grade level at her school, Allison can obtain a sample that includes a variety of ages, genders, and backgrounds.

This can help to ensure that the sample is representative of the population she is interested in studying.

Option (a) : is not a random sample because it only includes teenagers who happen to be at the grocery store at the time Allison is conducting her survey. This may not represent entire population of teenagers at her school.

Option (b) : is not a random sample either because it only includes people who happen to be at the library on Saturday morning. This may not be representative of the entire population of teenagers at her school.

Option (d) :  is not a random sample because it only includes teenagers from 20 different countries. This may not be representative of the population of teenagers at Allison's school or in her local area.

Therefore, the correct option is (c).

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The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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Answer:

12.5% chance

Step-by-step explanation:

First a spinner has a 25% chance of landing on a one, then a tails is a 50% chance, subtract devide 25 by two and you get 12.5.

Answer:

Rational.

Step-by-step explanation:

-5 times √121

= -5 * 11

=-55

Rational.

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

$127 is the answer.. can i have a brainliest? :)

The detailed answer of this question is:

P(X > 100 | X > 50)=0.455

Given that X follows an exponential distribution, we know that the probability density function (PDF) of X is given by:

f(x) = λe^(-λx) for x ≥ 0

where λ is the rate parameter of the distribution.

We are given that P(X < 50) = 0.25. Using the cumulative distribution function (CDF) of X, we can write:

P(X < 50) = 1 - e^(-λ*50) = 0.25

Solving this equation for λ, we get:

λ = -ln(0.75)/50 ≈ 0.0278

Now, we are asked to find P(X > 100 | X > 50). Using the definition of conditional probability, we can write:

P(X > 100 | X > 50) = P(X > 100 and X > 50) / P(X > 50)

= P(X > 100) / P(X > 50)

= e^(-λ100) / e^(-λ50)

= e^(-λ*50)

Substituting the value of λ, we get:

P(X > 100 | X > 50) = e^(-0.0278*50) ≈ 0.455

Therefore, the probability that a high-risk driver will have an accident after 100 days given that they have not had an accident for the first 50 days is approximately 0.455.

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Answer:

Step-by-step explanation:

cant see pic

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer:

$524.30

Step-by-step explanation:

70+60+25+350+30= 535

535*.02(20%)

10.7

535-10.7=

524.3

Answer:

$107

Step-by-step explanation:

First you have to add up the costs and you get a total of $535

Then you need to make 535 equivalent to 100 then divide by 20 to get 107

Hope that helps and have a great day!

Answer:D or 99

Step-by-step explanation:

38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.

The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:

d =\(\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }\)

There are points that correspond to each vertex in the polygon:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:

d =\(\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }\) ≤ b r/≥ d=\(\sqrt{(8-(-2)^{2})+(7-11)^{2} }\)  ≤b r/≥

d=\(\sqrt{116}\)

There are points that correspond to each vertex in the polygon:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So, using the distance formula and the vertex positions of side PT, we can determine its length:

P  = (-2, 11)

T  = (8, 7)

The length of PT is \(\sqrt{116}\)

The other 4 sides are handled in the same way, and the results are as follows:

TS = \(\sqrt{49}\)

SR = \(\sqrt{50}\)

RQ = \(\sqrt{61}\)

QP = \(\sqrt{40}\)

You may calculate the perimeter by adding all the sides:\(\sqrt{116}\)+\(\sqrt{49}\)+\(\sqrt{50}\)+\(\sqrt{61}\)+\(\sqrt{40}\) = 38.97

The solution is 39 units if you round off.

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The factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

It is given that For every part produced by a factory there are 5 ounces of scrap aluminum that can be recycled there are 16 ounces in 1 pound and 2,000 in 1 ton we need to find how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling

What is a Ratio?

A quantitative relation between two amounts showing the number of times one value contains in another

1 part produced  ⇒ 5 ounces scrap aluminium recycled.

So, the ratio of parts produced : Scrap of aluminium = 1   : 5  .... (a)

Let us assume for m parts produced ,  1 ton of scrap is recycled.

Also, 1 ton = 2, 000 pounds

and 1 pound = 16 ounces

⇒ 1 ton = 2000 x (16 ounces)  = 32,000 ounces

So, for m parts made in the  factory, 32,000 ounces scrap is recycled.

So, the ratio of parts produced : Scrap of aluminium =  m   : 32,000  .... (b)

From both the given ratio, we get

1   : 5  = m   : 32,000

m=32000/5

m=6400

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An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

3.5 hours for 1 cake means 3.5 hours per cake.

similar : 2 hours for 1 pie means 2 hours per pie.

so, if there are e.g. 3 pies, they take 3×2 = 6 hours.

therefore the general constraint is

3.5x1 + 2x2 <= 70

I think the names "x1" and "x2" are confusing when writing this inequality.

I prefer to use x and y.

and then it would look like

3.5x + 2y <= 70

Answer: A

Step-by-step explanation: -20

Answer:

74 fishes

Step-by-step explanation:

Total number of people = 1672

Let us represent:

Number of people over the age of 50 = a

Number of people below the age of 50 = b

People over the age of 50 she gave = 16 fish

People below 50 she gave = 96 fish. Only 3/4 of the over 50s collected their salmon

= 3/4a collected fish = 0.75a

If a should collect = 96 fishes

0.75a =

Cross Multiply

=0.75a × 96 fishes/ a

= 72 fishes

Therefore, 3/4 of the over 50s collected 72 fishes.

1/8 of the under 50s collected their fish.

= 1/8b collected fish = 0.125b

If b people should collect = 16 fishes

0.125b people =

Cross Multiply

0.125b × 16 fishes/b

= 2 fishes.

Therefore, the total number of fishes shared

= 72 fishes + 2 fishes

= 74 fishes